4
QuizMultiple Choice

Solving Systems of Linear Equations: Linear Combinations — Quiz

Question 4 • Algebra I

The system of equations is solved using the linear combination method. 1 half x plus 4 y is equal to 8 which is same as negative 2 times 1 half x plus 4 y is equal to 8 which is same as negative x minus 8 y is equal to negative 16; 3 x plus 24 y is equal to 12 which is same as 1 third times 3 x plus 24 y is equal to 12 which is same as x plus 8 y is equal to 4; negative x minus 8 y is equal to negative 16 is added to x plus 8 y is equal to 4 which results 0 is equal to negative 12 What does 0 is equal to negative 12 mean regarding the solution to the system?

Answer
A
There are no solutions to the system because the equations represent the same line.
B
There are infinitely many solutions to the system because the equations represent the same line.
C
There are infinitely many solutions to the system because the equations represent parallel lines.
D
There are no solutions to the system because the equations represent parallel lines.

Explanation

The elimination steps produce 0 = −12, which is false. That means the equations cannot both be true for any ordered pair, so the system has no solution. The original equations have different constant terms after their left sides are scaled to match, so they represent distinct parallel lines, not the same line.

AI-written and checked against the verified answer.

Previous
Next